1. Tardigrade
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  4. A point traversed half of the distance with a velocity v0. The half of remaining part of the distance was covered with velocity v1 second half of remaining part by v2 velocity. The mean velocity of the point, averaged over the whole time of motion is

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Q. A point traversed half of the distance with a velocity $v_0$. The half of remaining part of the distance was covered with velocity $v_1$ & second half of remaining part by $v_2$ velocity. The mean velocity of the point, averaged over the whole time of motion is

Motion in a Straight Line

Solution:

Let the total distance be $d$.
Then for first half distance, time $=\frac{d}{2 v_0}$, next distance.
$=v_1 t$ and last half distance $=v_2 t$
$\therefore v _1 t + v _2 t =\frac{ d }{2} ; t =\frac{ d }{2\left( v _1+ v _2\right)}$
Now average speed
$t=\frac{d}{\frac{d}{2 v_0}+\frac{d}{2\left(v_1+v_2\right)}+\frac{d}{2\left(v_1+v_2\right)}}$
$=\frac{2 v_0\left(v_1+v_2\right)}{\left(v_1+v_2\right)+2 v_0}$